A Strain-Based Rectangular Finite Element for Accurate Static and Free Vibration Analysis of Thin Isotropic and Functionally Graded Plates

This study presents a novel strain-based rectangular plate finite element, denoted as SBRPFE20, developed for the accurate analysis of thin plate bending problems. The formulation is established within the framework of Kirchhoff plate theory and incorporates a coupled strain-based membrane–bending approach to effectively capture the interaction between bending and in-plane responses, particularly in functionally graded materials. Unlike existing strain-based plate elements, the proposed formulation is specifically developed to accurately model functionally graded material (FGM) plates, accounting for the continuous variation of material properties through the thickness. The proposed element employs four corner nodes with essential kinematic degrees of freedom and is designed to achieve high accuracy while maintaining computational efficiency. The performance of the SBRPFE20 element is systematically assessed through a comprehensive set of numerical benchmarks, including static bending and free vibration analyses of isotropic and functionally graded plates under various loading conditions, boundary configurations, and geometrical complexities. The numerical results demonstrate that the proposed element exhibits rapid and smooth convergence, excellent numerical stability, and superior accuracy compared with well-established finite elements available in the literature. The formulation demonstrates a locking-free behavior, particularly in the thin plate limit, and does not exhibit spurious stiffness effects, as confirmed through convergence studies and mesh distortion analyses. Owing to its robustness, efficiency, and accuracy, the SBRPFE20 element provides a reliable and effective tool for the static and dynamic analysis of thin isotropic and functionally graded plates.